Revisit the Poynting vector in PT-symmetric coupled waveguides

TL;DR

This paper revisits the Poynting vector in PT-symmetric waveguides, revealing that the traditional time-averaged Poynting vector cannot explain stopped light at exceptional points, and proposes a new formula based on complex fields.

Contribution

It introduces a new formula for group velocity in non-Hermitian systems using the original Poynting vector definition, resolving paradoxes in PT-symmetric optics.

Findings

Time-averaged Poynting vector is always positive in PT-symmetric waveguides.

The new formula explains both stopped and fast light near exceptional points.

Bridges classical electrodynamics with non-Hermitian physics.

Abstract

We show that the time-averaged Poynting vector in parity-time (PT ) symmetric coupled waveguides is always positive and cannot explain the stopped light at exceptional points (EPs). In order to solve this paradox, we must accept the fact that the fields E and H and the Poynting vector in non-Hermitian systems are in general complex. Based on the original definition of the instantaneous Poynting vector, a formula on the group velocity is proposed, which agrees perfectly well with that calculated directly from the dispersion curves. It explains not only the stopped light at EPs, but also the fast-light effect near it. This investigation bridges a gap between the classic electrodynamics and the non-Hermitian physics, and highlights the novelty of non-Hermitian optics.